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     "source": [
      "Modeling a Zombie Apocalypse\n",
      "============================\n",
      "\n",
      "This example demonstrates how to solve a system of first order ODEs\n",
      "using SciPy. Note that a Nth order equation can also be solved using\n",
      "SciPy by transforming it into [a system of first order\n",
      "equations](http://en.wikipedia.org/wiki/Ordinary_differential_equation#Reduction_to_a_first_order_system).\n",
      "In a this lighthearted example, a system of ODEs can be used to model a\n",
      "\"zombie invasion\", using the equations specified in [Munz et al.\n",
      "2009](http://mysite.science.uottawa.ca/rsmith43/Zombies.pdf).\n",
      "\n",
      "The system is given as:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "dS/dt = P - B*S*Z - d*S\n",
      "dZ/dt = B*S*Z + G*R - A*S*Z\n",
      "dR/dt = d*S + A*S*Z - G*R"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "with the following notations:\n",
      "\n",
      "*  S: the number of susceptible victims\n",
      "*  Z: the number of zombies\n",
      "*  R: the number of people \"killed\"\n",
      "*  P: the population birth rate\n",
      "*  d: the chance of a natural death\n",
      "*  B: the chance the \"zombie disease\" is transmitted (an alive person becomes a zombie)\n",
      "*  G: the chance a dead person is resurrected into a zombie\n",
      "*  A: the chance a zombie is totally destroyed"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This involves solving a system of first order ODEs given by: d**y**/dt =\n",
      "**f**(**y**, t)\n",
      "\n",
      "Where **y** = [S, Z, R].\n",
      "\n",
      "The code used to solve this system is below:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# zombie apocalypse modeling\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "from scipy.integrate import odeint\n",
      "plt.ion()\n",
      "plt.rcParams['figure.figsize'] = 10, 8\n",
      "\n",
      "P = 0\t    # birth rate\n",
      "d = 0.0001  # natural death percent (per day)\n",
      "B = 0.0095  # transmission percent  (per day)\n",
      "G = 0.0001  # resurect percent (per day)\n",
      "A = 0.0001  # destroy percent  (per day)\n",
      "\n",
      "# solve the system dy/dt = f(y, t)\n",
      "def f(y, t):\n",
      "\tSi = y[0]\n",
      "\tZi = y[1]\n",
      "\tRi = y[2]\n",
      "\t# the model equations (see Munz et al. 2009)\n",
      "\tf0 = P - B*Si*Zi - d*Si\n",
      "\tf1 = B*Si*Zi + G*Ri - A*Si*Zi\n",
      "\tf2 = d*Si + A*Si*Zi - G*Ri\n",
      "\treturn [f0, f1, f2]\n",
      "\n",
      "# initial conditions\n",
      "S0 = 500.     \t\t# initial population\n",
      "Z0 = 0        \t\t# initial zombie population\n",
      "R0 = 0        \t\t# initial death population\n",
      "y0 = [S0, Z0, R0]\t# initial condition vector\n",
      "t  = np.linspace(0, 5., 1000) \t# time grid\n",
      "\n",
      "# solve the DEs\n",
      "soln = odeint(f, y0, t)\n",
      "S = soln[:, 0]\n",
      "Z = soln[:, 1]\n",
      "R = soln[:, 2]\n",
      "\n",
      "# plot results\n",
      "plt.figure()\n",
      "plt.plot(t, S, label='Living')\n",
      "plt.plot(t, Z, label='Zombies')\n",
      "plt.xlabel('Days from outbreak')\n",
      "plt.ylabel('Population')\n",
      "plt.title('Zombie Apocalypse - No Init. Dead Pop.; No New Births.')\n",
      "plt.legend(loc=0)\n",
      "\n",
      "# change the initial conditions\n",
      "R0 = 0.01*S0   # 1% of initial pop is dead\n",
      "y0 = [S0, Z0, R0]\n",
      "\n",
      "# solve the DEs\n",
      "soln = odeint(f, y0, t)\n",
      "S = soln[:, 0]\n",
      "Z = soln[:, 1]\n",
      "R = soln[:, 2]\n",
      "\n",
      "plt.figure()\n",
      "plt.plot(t, S, label='Living')\n",
      "plt.plot(t, Z, label='Zombies')\n",
      "plt.xlabel('Days from outbreak')\n",
      "plt.ylabel('Population')\n",
      "plt.title('Zombie Apocalypse - 1% Init. Pop. is Dead; No New Births.')\n",
      "plt.legend(loc=0)\n",
      "\n",
      "# change the initial conditions\n",
      "R0 = 0.01*S0   # 1% of initial pop is dead\n",
      "P  = 10        # 10 new births daily\n",
      "y0 = [S0, Z0, R0]\n",
      "\n",
      "# solve the DEs\n",
      "soln = odeint(f, y0, t)\n",
      "S = soln[:, 0]\n",
      "Z = soln[:, 1]\n",
      "R = soln[:, 2]\n",
      "\n",
      "plt.figure()\n",
      "plt.plot(t, S, label='Living')\n",
      "plt.plot(t, Z, label='Zombies')\n",
      "plt.xlabel('Days from outbreak')\n",
      "plt.ylabel('Population')\n",
      "plt.title('Zombie Apocalypse - 1% Init. Pop. is Dead; 10 Daily Births')\n",
      "plt.legend(loc=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "<matplotlib.legend.Legend at 0x392ac90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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MxDAMTp8+zQ033EBGRgbe3t707duXbt268eqrrwKwb98+2rdvz4ULFzh8+DBN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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x35adc10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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+TzGWbNQoxVUAiNTJ5buXMX3HdPgs80HM3Rj8MOQH3Hj1BuYFzWMR00AsY2pg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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3787590>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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QMHr0aOjq6uK3334DAKSkpMDd3R35+flo3bo1AGDBggVIT09HWFgYQkND8ccf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\nsHLlStNxpArCwsJITU3lrrvuuun9XGZk7OoNYX19fcs2hBXXEBcXR+P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       "text": [
        "<matplotlib.figure.Figure at 0x38fcad0>"
       ]
      }
     ],
     "prompt_number": 1
    }
   ],
   "metadata": {}
  }
 ]
}